= Radial homotopy primitive near a zero section
{title2=$d\eta=\delta-H_0^*\delta$}
On a fiberwise star-shaped neighborhood, let $H_s$ scale fibers by $s$ and let $E$ be the radial <vector field>. For a <closed differential form> $\delta$ with zero pullback to the <zero section>, the homotopy primitive $\eta=\int_0^1s^{-1}H_s^*(\iota_E\delta)\,ds$ satisfies $d\eta=\delta$. For a two-form, it vanishes as an ambient covector along that section, providing the fixed-submanifold condition in the <relative Moser theorem>.
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